Work

Heisenberg uniqueness pairs and the wave equation

Year: 2025

Type: article

Abstract: The concept of the Heisenberg uniqueness pair was introduced by Hedenmalm and Montes‐Rodríguez as a variant of the uncertainty principle for the Fourier transform. The main results in Hedenmalm and Montes‐Rodríguez (Ann. of Math. (2) 173 (2011), 1507–1527) concern the hyperbola () and lattice‐crosses (), where it is proved that is a Heisenberg uniqueness pair if and only if . In this paper, we study the endpoint case ( in ) and investigate the minimal information required on the zero set to form such a pair. When is contained in the union of two curves in the plane, we provide characterizations using dynamical system conditions. The situation differs in higher dimensions, where we obtain characterizations when is the union of two hyperplanes.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70095

Authors: Shanlin Huang, Jiaqi Yu

Institutions: Sun Yat-sen University, Huazhong University of Science and Technology

Language: English

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: National Natural Science Foundation of China

Awards: G5404121423, G6262907380